Thickness measuring apparatus and method

ABSTRACT

A measuring system including a linear gauge  8  is placed on a vibration isolation table  7 , and this system assembly is placed in a temperature controllable, constant-temperature chamber. A specimen table  16 , which has a centrally-disposed circular protrusion  16 C of a diameter sufficiently smaller than a specimen under measurement, is mounted on a surface plate  2  of a linear gauge  8 . The position of a measuring element  1  is measured when it is brought into contact with the centrally-disposed circular protrusion  16 C, and the position of the measuring element  1  is measured when it is brought into contact with the specimen placed on the specimen table. The measured values are used to determine the thickness of the specimen.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to a method and apparatus formeasuring the thicknesses of various materials efficiently andprecisely.

[0002] At present, it is a laser thickness measuring machine for blockgauge calibration use that is traceable and capable of measuringmaterial thicknesses with the highest precision. Because of itsapplication specified for block gauge measurements, however, the laserthickness measuring machine has a limitation on the size of the specimento be measured. Further, the laser thickness measuring machine calls forsufficient knowledge and much skill, in particular, for precisemeasurement of the thickness of a transparent material like glass or asilicon (Si) single crystal with oxidized surface, since a phase shiftoccurs when the laser light is reflected from such a measuring object orspecimen. Additionally, the laser thickness measuring machine isexpensive.

[0003] For the reasons given above, a contact measuring method is widelyused to measure the thicknesses of various materials through utilizationof a linear gauge or the like. A conventional measuring system usingsuch a method comprises, as depicted in FIG. 1, a measuring element 1, athickness surface plate 2, and, if necessary, an auxiliary jig 4 that isused to provide increased repeatability or accuracy of measurement. Themeasuring system is placed on a vibration isolation table, and themeasurement is conducted in a constant temperature room. The measuringtemperature is usually 20±1° C., preferably, 20±0.5° C. for measurementwith higher accuracy. An ordinary measurement procedure begins withbringing the measuring element 1 into contact with the surface of thesurface plate 2 as depicted in FIG. 1A (or the auxiliary jig 4 in FIG.1C) to define a reference point for measurement. The next step is toplace a measuring object or specimen 3 on the surface plate 2 asdepicted in FIG. 1B (or the auxiliary jig 4 in FIG. 1C), followed bybringing the measuring element 1 into contact with the specimen 3.Disposed between the surface plate 2 and the specimen 3 in FIG. 1C isthe auxiliary jig 4 that has a vacuum-suction capability and henceensures fixing the specimen 3 for stable measurement. In this instance,the thickness of the specimen 3 is measured as the distance from thereference point to the tip of the measuring element 1.

[0004] In many cases, the accuracy of the linear gauge in the thicknessmeasuring machine using the above-described method is used intact as theaccuracy of the thickness measurement.

[0005] In the actual measuring system, however, the accuracy ofmeasurement is influenced, for example, by the rigidity of a thicknessgauge stand, or the flatness of the surface plate 2, the flatness andparallelism of the auxiliary jig 4 and the specimen 3, and a warp in thespecimen 3. The specimen 3 may sometimes be measured while left curvedas depicted in FIG. 2. The measuring accuracy is affected as well bydistortion of the specimen 3 that is caused by its contact with themeasuring element 1 or auxiliary jig 4. This incurs the possibility thatthe difference between the measured value and the true thickness of thespecimen 3 is fairly larger than the accuracy guaranteed by themeasuring system.

[0006] Further, a stable measuring environment is indispensable foraccurate thickness measurement, but occasionally the prior art does notgive due consideration in this respect. In particular, the stability ofthe measuring temperature, the absence or presence of vibration, and thecleanness of the measuring room greatly affect the accuracy ofmeasurement, and hence much attention should be paid to them. Themeasurement is usually carried out in a constant temperature room, andthe stable point of room temperature varies with the numbers of peopleand in-service devices in the room, and the local temperature in theroom fluctuates with comings and goings of people and ON/OFF operationsof devices installed in the room. On this account, the temperaturestable point during measurement, which affects the accuracy ofmeasurement, undergoes about ±1° C. variations with measurementconditions, allowing temperature fluctuations during measurement. Forexample, in the case of measuring a block gauge of a 10 mm nominal size[Literature 1] with a ±0.5° C. temperature stability, its linearexpansion coefficient of approximately ±10⁻⁵ K⁻¹ may sometimes cause ameasurement error of around ±0.05 μm.

[0007] As described above, the prior art has many problems that shouldbe taken into account for contact thickness measurement with “highaccuracy,” and hence it does not allow ease in measuring accurately to±0.1 μm.

SUMMARY OF THE INVENTION

[0008] It is therefore an object of the present invention to provide amethod and device for measuring absolute values of the thicknesses ofvarious materials efficiently and precisely.

[0009] The thickness measuring apparatus according to the presentinvention comprises:

[0010] a constant-temperature chamber;

[0011] a vibration isolation table placed in said constant-temperaturechamber;

[0012] a linear gauge provided with a surface plate mounted on saidvibration isolation table and a measuring element for contacting aspecimen under measurement mounted on said surface plate from above, foroutputting information about the position of said measuring element; and

[0013] a specimen table mounted on said surface plate and having acentrally-disposed circular protrusion for receiving said specimen, saidcentrally-disposed circular protrusion having a flat surface of adiameter sufficiently smaller than said specimen.

[0014] The thickness measuring method according to the present inventioncomprises the steps of:

[0015] (a) bringing down said measuring element of said linear gaugefrom above into contact with a centrally-disposed circular protrusion ofa specimen table mounted on said surface plate to measure the positionof said measuring element as a first position, said centrally-disposedcircular protrusion having a diameter sufficiently smaller than saidspecimen;

[0016] (b) mounting said specimen on said centrally-disposed circularprotrusion and bringing down said measuring element of said linear gaugefrom above into contact with said specimen to measure the position ofsaid measuring element as a second position; and

[0017] (c) calculating the thickness of said specimen from the first andsecond positions.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1A is a diagram schematically showing the state in which ameasuring element is held in contact with a measuring gauge surfaceplate according to a conventional thickness measuring method;

[0019]FIG. 1B is a diagram schematically showing the state in which themeasuring element is held in contact with a specimen under measurement;

[0020]FIG. 1C is a diagram schematically showing an example of using anauxiliary jig for measurement;

[0021]FIG. 2 is a schematic diagram explanatory of problems of theconventional measuring method;

[0022]FIG. 3 is a diagram schematically illustrating an embodiment ofthe present invention intended to stabilize measuring environments;

[0023]FIG. 4 is a diagram schematically depicting another embodiment ofthe present invention intended for further stabilization of temperatureby covering the measuring element and the specimen under measurementwith a case or the like to place them in a closed or semiclosed space;

[0024]FIG. 5A is a side view of a specimen table for use in the presentinvention;

[0025]FIG. 5B is its plan view;

[0026]FIG. 5C is a schematic diagram of another example of the specimentable;

[0027]FIG. 6 is a diagram explanatory of dimensions of the specimentable;

[0028]FIG. 7 is a schematic diagram for explaining the thicknessmeasuring method according to the present invention;

[0029]FIG. 8 is a graph showing the measured values of the thickness ofa synthetic quartz glass substrate by a conventional method and by thisinvention method;

[0030]FIG. 9 is a flowchart for explaining how to correct measured valuefor the influence of distortion caused by the contact of the measuringelement with the specimen and the specimen table;

[0031]FIG. 10A is a schematic diagram for explaining the measurement ofthe reference position of the measuring element;

[0032]FIG. 10B is a schematic diagram for explaining the measurement ofthe position of the measuring element on the specimen when the latter isplaced on the specimen table;

[0033]FIG. 11 is a graph showing numerical values of distortion causedby the contact of the measuring element with specimens of syntheticquartz glass and Si single crystal;

[0034]FIG. 12 is a graph showing the measured values of the thickness ofa synthetic quartz glass substrate;

[0035]FIG. 13 is a graph showing calculated values of the amount ofdistortion when the thickness of the Si single crystal specimen wasmeasured using a specimen table made of synthetic quartz glass and theamount of distortion when the thickness of the synthetic quartz glassspecimen was measured using a specimen table made of Si single crystal;and

[0036]FIG. 14 is a graph showing the measured values of the thickness ofa (111) Si single crystal substrate; and

[0037]FIG. 15 is a graph showing measured results of Class K block gaugeby this invention method.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0038] A description will be given first of stabilization of themeasurement environment.

[0039]FIG. 3 is a schematic diagram illustrating the entire structure ofthe thickness measuring apparatus according to the present invention.The thickness measurement is conducted in a constant-temperature chamber5 held in a clean environment. This excludes the influence of dust andhence provides increased measuring accuracy and avoids the need forcleaning a linear gauge 8 and a specimen under measurement 3 (notshown), raising the working efficiency as well. The entire measuringsystem including the linear gauge 8 is mounted on a vibration isolationtable 7 to exclude the influence of vibration on measurement. Further,the measuring system and the vibration isolation table 7 are placed intheir entity in the constant-temperature chamber 5.

[0040] The temperature in the constant-temperature chamber 5 can be setat a desired value by a temperature controller 13 of temperaturesettings from 18 to 28° C. with 0.001° C. resolution. The temperature inthe constant-temperature chamber 5 is measured by a temperature sensor14 using a platinum resistance thermometer, and the measured value isprovided to the temperature controller 13. From the top of theconstant-temperature chamber 5, temperature-controlled air is suppliedby a spot air conditioner 6 into the chamber 5 through a blast duct 10and a filter 12. The filter 12 not only removes dust in the air but alsoserves as a buffer against the supplied airflow to make it uniform andconsistent. The air discharged from the lower portion of the chamber 5is returned to the spot air conditioner 6 through an exhaust duct 11.The air returned to the spot air conditioner 6 is cooled by a coolerdisposed therein and then heated again by a heater. The air suppliedfrom the spot air conditioner 6 is subjected to PID (Proportional plusIntegral plus Derivative) control by the temperature controller 13 sothat the temperature at the position of the temperature sensor 14 (atthe control point) in the constant-temperature chamber 5 always remainsat the set value.

[0041] Needless to say, the temperature stability in the chamber 5 canbe further increased by using a material of excellent thermal isolationfor the chamber 5 and stabilizing the temperature outside it. With thetemperature in the chamber 5 thus stabilized, it is possible to keep thetemperature of the specimen 3 at a constant value, for instant, at23±0.01° C., at all times, ensuring accurate measurements in a stabletemperature environment. With the conventional measuring apparatus usingonly a constant-temperature room without the above-mentioned temperaturecontrol by the airflow, when the measuring temperature is changed fromthe reference temperature so as to measure the linear expansioncoefficient or the like in the vicinity of room temperature, temperaturestabilization consumes much time, causing the problem of putting anappreciable load on a measurer; but the FIG. 3 structure permitsreduction of the time for temperature stabilization, and hencefacilitates measurements.

[0042]FIG. 4 is a schematic showing of the inside of thetemperature-constant chamber 5 depicted in FIG. 3. The surface plate 2of the linear gauge 8 is placed on the vibration isolation table 7, anda specimen table 16 having a circular central protrusion 16C is mountedon the surface plate 2. Disposed above the specimen table 16 is avertically moving measuring element 1 of the linear gauge 8. Thespecimen under measurement 3 is placed, though not shown, on the centralprotrusion 16C of the specimen table 16. By covering the linear gauge 8,the specimen table 16 and their surroundings with a case 15 made usingpolyethylene or plastics film, or acrylic plate to keep them in asemiclosed space as shown in FIG. 4—this excludes the influence of theairflow in the chamber 5, ensuring further temperature stabilization.With the measuring system placed in its entirety in aconstant-temperature clean room, it is possible to further improve themeasuring environment and hence provide increased reliability inmeasurements.

[0043] The specimen table 16, on which the specimen 3 is mounted formeasuring its thickness, is intended to reduce errors in the measuringsystem. FIG. 5A is a side view of the specimen table 16 and FIG. 5B isits plan view. The specimen table 16 has the protrusion 16C protrudingcentrally thereof from the table surface optically polished with highflatness and parallelism. In the illustrated example, the circularcentral protrusion 16C is formed by etching so that it is about 8 mmacross and tens of micrometers (μm) high. Alternatively, the centralprotrusion 16C may be tapered outwardly in its radial direction asdepicted in FIG. 5C.

[0044] The diameter and height of the central protrusion 16C need to bewithin the following ranges. In such a model as depicted in FIG. 6, theradius of curvature R of warp of the specimen 3 is given by thefollowing equation. $\begin{matrix}{R = {\frac{\left( {a/2} \right)^{2} + b^{2}}{2b} \approx {\frac{1}{2b}{\left( \frac{a}{2} \right)^{2}\quad\lbrack{mm}\rbrack}}}} & (1)\end{matrix}$

[0045] where a is the size of the specimen and b is the severity ofwarp. Setting a permissible error b′ at 0.05 μm, the diameter d of thecentral protrusion 16C needs to be within such a range as given by thefollowing equation, $\begin{matrix}{d < {2\sqrt{{1.0 \times 10^{- 4}R} - {2.5 \times 10^{- 5}}}} \approx {\frac{1}{50}{\sqrt{R}\quad\lbrack{mm}\rbrack}}} & (2)\end{matrix}$

[0046] Assuming that the specimen is a disc approximately 50 mmφ indiameter and the value b of warp is 2 μm or so, it follows from Eq. (2)that the diameter d of the central protrusion 16C of the specimen table16 must be less than about 8 mm. The height h of the central protrusion16C needs to be larger than the magnitude b of warp; it is recommendedthat the height h be 10 μm or more so as to ensure accurate measurementuntil b=5 μm. At any rate, it is necessary that the central protrusion16C be sufficiently smaller in diameter than the specimen 3 andsufficiently larger in height than the warp of the specimen 3.

[0047] By minimizing the direct contact area with the specimen 3, it ispossible to minimize the influence of the flatness and parallelism ofthe specimen 3 and the specimen table 16 or the surface configuration ofthe specimen 3 on the measurement, enhancing the repeatability of themeasurement. It is desirable that the specimen table 16 be made of thesame material as that of the specimen 3 for the reasons given later on.

[0048] Now, a description will be given, with reference to FIG.7, of thethickness measuring method in the case of using the specimen table 16.The specimen table 16 is firmly fixed to the surface plate 2 by means ofan auxiliary jig 17 that possesses a double-sided vacuum suctioncapability. The specimen table 16 thus held tightly on the surface plate2 ensures stabilization of measured values and provides enhancedrepeatability of measurement. To begin with, the measuring element 1 isextended down into direct contact with the central protrusion 16C of thespecimen table 16 under a fixed load as indicated by the broken linesP1. Then, a counter of the linear gauge 8 is reset to a reference point(zero point). Next, the measuring element 1 is brought up, and thespecimen 3 is placed on the central protrusion 16C of the specimen table16, after which the measuring element 1 is brought down again intodirect contact with the specimen 3 under the same load as mentionedabove as indicated by the broken lines P2.

[0049] When the specimen 3 is a transparent material, an abnormality inthe state of contact between the specimen table 16 and the specimen 3due to warp of the latter can be detected through observation of theshape of an interference fringe. Hence, the state of contact between thespecimen 3 and the specimen table 16 can be checked, and consequently,highly reliable measurements can be achieved. The thickness of thespecimen 3 is measured as the distance from the reference point to thepoint of the measuring element 1. After this, the specimen 3 is removedfrom the specimen table 16, then a check is made to see if the referencepoint goes back to zero, and the measurement is completed. If thereference point does not return to zero, it is regarded that an erroroccurred during measurement, and the data obtained in this session ofmeasurement is not used. This procedure is repeated to verify therepeatability of measurement and the measuring accuracy.

[0050] Next, a description will be given of an example of thicknessmeasurement using the specimen table 16 according to the presentinvention. This example used a linear gauge having an accuracy of ±0.03μm and a resolution of ±0.005 μm. The linear gauge used allows itscontact pressure for measurement to change to 0.91, 104, 1.07, 1.22 and1.5 N. The tip of the measuring element 1 was made of a superhard alloyof the tungsten carbide series and its curvature of radius R₀ was 1.6mm. The specimen table 16 was made of synthetic quartz glass. Thespecimen 3 was a synthetic quartz glass substrate. The temperature nearthe specimen 3 during measurement was set at 23° C. or so. For thepurpose of comparison, the specimen 3 was measured by the conventionalmethod that did not use the specimen table 16.

[0051] Since the specimen 3 is warped in some cases as shown in FIG. 2,thickness of the specimen 3 was measured a total of 10 times: 5 timeswith the one side upward and 5 times the other side upward. The contactpressure for measurement was set at 0.91 N. FIG. 8 shows the measuredresults. The temperature near the specimen during measurements alwaysremained constant at 22.97±0.09° C. In each measurement the counter ofthe linear gauge 8 was in a stable condition with the highest resolutiondisplayed stably at 0.005 μm. In FIG. 8, the circles indicate themeasured values obtained by repeatedly measuring the thickness of thespecimen 3 with the conventional method. The repeatability ofmeasurement by the prior art method was ±0.15 μm or so, and the averagevalue of the measured values was 5004.60 μm. The squares indicatemeasured value obtained by repeatedly measuring the thickness of thespecimen 3 placed on the specimen table 16 according to the presentinvention. The white squares indicate the measured value obtained withthe surface of the specimen 3 held upward, whereas the black squaresindicate the measured value obtained with the back of the specimen 3held upward. The repeatability was approximately ±0.02 μm and theaverage value of the measured was 5003.75 μm.

[0052] No substantial differences are found between thethickness-measured values indicated by the white and black squares,which demonstrates the effect of the specimen table according to thepresent invention. If the difference in repeatability between the twokinds of measured values is in excess of ±0.02 μm or so, however, it isconsidered that slight warpwarp of the specimen affected themeasurement, and the measured value smaller than the other should beadopted. The measured values by the present invention method are smalleraround 1 μm than the measured value by the conventional method, and itcan be seen that the repeatability of the measured values obtained withthe specimen 3 repeatedly mounted on the specimen table 16 is alsohigher than the repeatability by the prior art method.

[0053] Next, a description will be given of the influence of distortionon the thickness measurement.

[0054] To measure the true thickness of the specimen 3, it is necessaryto exclude the influence of distortion caused by the contact of themeasuring element 1 with the specimen table 16 and the specimen 3. Amethod for excluding the influence of such distortion on the measurementwill be described below. FIG. 9 is flowchart showing the procedure to befollowed to correct measured values.

[0055] In the first place, the materials of the specimen table 16 andthe specimen 3 are checked (step S1). When the specimen table 16 and thespecimen 3 are made of the same material, the amounts of distortionoccurring in them are equal, and consequently, the influences ofdistortion are cancelled each other. Accordingly, the measurement valueis not affected by distortion, and hence it need not be corrected (stepS2). When the specimen table 16 and the specimen 3 are made of differentmaterials, the amounts of distortion occurring in them differ due to thedifference in elastic characteristic between their materials. In thisinstance, the measurement value is affected by distortion, and henceneeds to be corrected (step S3). The amount of distortion is given bythe following equation called Hertz's formula. $\begin{matrix}{\delta = \sqrt[3]{\frac{9}{16}\frac{1}{R_{0}}\left( {\frac{1 - \sigma_{1}^{2}}{E_{1}} + \frac{1 - \sigma_{2}^{2}}{E_{2}}} \right)^{2}P^{2}}} & (3)\end{matrix}$

[0056] where δ is distortion, R₀ is the curvature of radius of the tipof the measuring element 1, σ₁ and σ₂ are Poisson's ratios, E₁ and E₂are Young's moduli, and P the contact pressure for measurement. Thesuffix 1 denotes the measuring elemental and 2 denotes the object (thespecimen table 16 or specimen 3) contacted by measuring element 1.

[0057] From the viewpoint of the measuring procedure, an error actuallycontained in the measurement value by distortion is such as describedbelow. To begin with, the measuring element 1 is brought into contactwith the specimen table 16 under a predetermined contact pressure asshown in FIG. 10A; and a distortion δ₀ is calculated by Eq. (3) from thecontact pressure and the height h₀ of the measuring element 1 ismeasured as a reference height. Next, the specimen 3 is mounted on thespecimen table 16 and the measuring element 1 is contacted with thespecimen 3 under the above-mentioned contact pressure as depicted inFIG. 10B. A distortion δ_(S) is calculated by Eq. (3) from the contactpressure and the height h₁ of the measuring element 1 is measured. Thetrue thickness t of the specimen 3 and its measured value t′ bear such arelationship as given by the following equation.

t=h ₀+δ₀−(h ₁+δ_(S))=t′−δ_(diff)  (4)

[0058] When the specimen table 16 and the specimen 3 are made of thesame material as referred to previously, δ₀=δ_(S), and δ_(diff)=0;hence, the measurement value need not be corrected for distortion.δ_(diff) can be calculated by the following equation by use of Eq. (3)(step S4). $\begin{matrix}{\delta_{diff} = {{\delta_{0} - \delta_{S}} = {\sqrt[3]{\frac{9}{16R_{0}}\left( {\frac{1 - \sigma_{1}^{2}}{E_{1}} + \frac{1 - \sigma_{2}^{2}}{E_{2}}} \right)^{2}P^{2}} - \sqrt[3]{\frac{9}{16R_{0}}\left( {\frac{1 - \sigma_{1}^{2}}{E_{1}} + \frac{1 - \sigma_{3}^{2}}{E_{3}}} \right)^{2}P^{2}}}}} & (5)\end{matrix}$

[0059] In Eq. (5), the suffix 1 denotes the measuring element 1, 2denotes the specimen table 16, and 3 denotes the specimen 3. Bysubtracting the value δ_(diff) from the measurement value as given inEq. (4), the true thickness can be obtained (step S5).

[0060] Incidentally, the Young's modulus and Poisson' ratio in theHertz's formula are defined for isotropic materials but not defined foranisotropic materials. However, by use of equivalent Young's moduli andPoisson's ratios, the distortion can be mathematically computed orexperimentally measured as described later on. FIG. 11 is a graphshowing examples of numerically calculated values of distortion causedby the contact of the measuring element 1 with synthetic quartz glassand Si single crystal. The Young's modulus and Poisson's ratio of thesynthetic quartz glass were set at 7.2×10¹⁰ N/m² and 0.16, respectively,and the Young's modulus and Poisson's ratio of the Si single crystalwere set at 13.0×10¹⁰ N/m² and 0.28, respectively. The tip of themeasuring element 1 was the same as used in the above-describedmeasurements; that is, the tip was made of superhard alloy of thetungsten carbide series and its radius of curvature R₀ was 1.6 mm. TheYoung's modulus and Poisson's ratio of the tip of the measuring element1 were 63.0×10¹⁰ N/m² and 0.20, respectively. It is apparent from FIG.11 that when contacted by the measuring element 1 under about 1 N thatis the minimum contact pressure for measurement of the linear gauge 8, adistortion of around 0.43 μm occurs in the synthetic quartz glass and adistortion of about 0.30 μm occurs in the Si single crystal. Theseresults suggest the influence of distortion needs to be taken intoaccount to achieve high measurement accuracy within ±0.1 μm.

[0061] A description will be given of examples of correcting thedistortion. The thickness measurements were conducted using the samemeasuring apparatus and measuring conditions as in the above. As thespecimen 3, a synthetic quartz glass substrate and a (111) Si singlecrystal substrate were prepared. And two kinds of specimen tables 16were prepared, one of which was made of synthetic quartz glass and theother of which was made of (111) Si single crystal. The thicknessmeasurements were conducted with the contact pressure P changed to 0.91,1.04, 1.07, 1.22 and 1.51 N.

[0062] In FIG. 12, black circles indicate the results of measurementsconducted for the synthetic quartz glass substrate. When the specimentable 16 made of the synthetic quartz glass is used, no distortioncompensation is required; the measured values hardly change with thecontact pressure P and stay within the range of 5003.75±0.01 μm. Whenthe specimen table 16 made of the Si single crystal is used, themeasurement value varies with the contact pressure P as indicated by theblack squares. In this instance, the measurement values are correctedfor distortion. White squares indicate distortion-corrected values ofthe measurement values indicated by the black squares. FIG. 13 shows theamounts of correction, expressed by Eq. (5), that were calculated usingthe contact pressure P as a parameter. The Young's moduli and Poisson'sratios of the synthetic quartz glass and the Si single crystal were thesame as those used in the above. The value δ_(diff) thus obtained is−0.14, −0.15, −0.15, -0.17 and −0.19 μm under the contact pressureP=0.91, 1.04, 1.07, 1.22 and 1,51 N. When corrected using these values,the measurement values became constant at 5003.78±0.02 μm independentlyof the contact pressure P. The value corrected for distortion is largerabout 0.03 μm than in the case where the specimen table 16 made ofsynthetic quartz glass was used. This is considered due to the factsthat wringing between the specimen table 16 and the specimen 3 changeswith their materials and that the Young's modulus and Poisson's ratio ofthe Si single crystal are calculated on the assumption that it isisotropic material in defiance of its anisotropy. When it becomespossible to handle the Si single crystal taking its anisotropy intoaccount, better correction will be expected.

[0063]FIG. 14 shows measured results for the (111) Si single crystalsubstrate. The black circles indicate the values measured with thespecimen table made of the synthetic quartz glass, and the white circlesindicate the values obtained by correcting the black-circled values fordistortion. The black squares indicate the values measured with thespecimen table made of the Si single crystal. When the specimen table 16made of the Si single crystal was used, the measured values hardly varywith the contact pressure P and are constant at 8399.62±0.01 μm. Whenthe specimen table 16 made of the synthetic quartz glass was used, themeasured value became constant at 8399.58±0.01 μm after corrected usingthe calculated values shown in FIG. 11. In this case, too, the measuredvalues differ by about 0.04 μm for the reasons that the two specimentables 16 were made of different materials and that the anisotropy ofthe single crystal was ignored as referred to previously.

[0064] The measurement results suggest that the specimen table 16 maypreferably be identical in material and in cut plane with the specimen3, but the above-described method permits reduction of the dependence ofthe measurement on the contact pressure P, achieving a measuringaccuracy of ±0.1 μm or so. While in the above the synthetic quartz glasshas been described as the material for the specimen table 16, otherglass materials or ceramics that can be regarded as isotropic may alsobe used.

[0065] Measurements were conducted by this invention method on a blockgauge that is a practical standard for length. A K-class block gauge ofthe highest calibration accuracy was used for measurement. The blockgauge was made of zirconia ceramic, and its nominal size was 5 mm andnominal value was 5000.07 μm. The calibration accuracy at the standardtemperature 20° C. is ±0.04 μm. The linear expansion coefficient is9.3±1.0×10⁻⁶ K⁻¹. The Young's modulus and Poisson's ratio of the blockgauge are 21.1×10¹⁰ N/m² and 0.30, respectively. The linear gauge 8 usedwas the same as in the measurements described above, and the measuringtemperature was set at 20° C. that is the standard measuring temperatureof the block gauge. The specimen table 16 was made of synthetic quartzglass. The contact pressure for measurement was changed to 0.91, 1.04,1.07, 1.22 and 1.51 N.

[0066]FIG. 15 shows measurement results. The black circles indicatemeasured values and white circles indicate values obtained by correctingthe black-circle measured values for distortion. The broken lineindicates the nominal value of the block gauge. The temperature near thespecimen 3 during measurement was constant at 19.98±0.09° C. An error inthe measured thickness value by the temperature variation of about 0.1°C. is approximately 0.005 μm calculated from the linear expansioncoefficient of zirconia ceramic. The repeatability of measurement was±0.02 μm. It can be seen from FIG. 15 that the values measured under therespective contact pressures, corrected for distortion, are constant at5000.09±0.01 μm. Since the nominal value is 5000.07 μm, the measuredvalues agree with the nominal value with a difference of only 0.02 μm orso therebetween. The calibration accuracy of the block gauge is ±0.04μm, from which it can be seen that the present invention permits highaccuracy thickness measurements.

EFFECT OF THE INVENTION

[0067] As described above, according to the present invention, it ispossible to conduct thickness measurement in a stable environment andlessen the influence of errors occurring in the measuring system andhence provide increased measurement repeatability and reliability.Further, the influence of distortion can be excluded by correction.Accordingly, the thicknesses of various materials can be measuredefficiently and accurately, and the accuracy and repeatability ofthickness measurement can be enhanced markedly.

What is claimed is:
 1. A thickness measuring apparatus comprising: aconstant-temperature chamber; a vibration isolation table placed in saidconstant-temperature chamber; a linear gauge provided with a surfaceplate mounted on said vibration isolation table and a measuring elementfor contacting a specimen under measurement mounted on said surfaceplate from above, for outputting information about the position of saidmeasuring element; and a specimen table mounted on said surface plateand having a centrally-disposed circular protrusion for receiving saidspecimen, said centrally-disposed circular protrusion having a flatsurface of a diameter sufficiently smaller that said specimen.
 2. Theapparatus of claim 1, wherein the diameter of said flat surface of saidcentrally-disposed circular protrusion is 8 mm or less.
 3. The apparatusof claim 1 or 2, wherein the height of said centrally-disposed circularprotrusion is 10 μm or more.
 4. The apparatus of claim 1 or 2, whereinsaid centrally-disposed circular protrusion is columnar.
 5. Theapparatus of claim 1 or 2, wherein said centrally-disposed circularprotrusion is tapered outwardly in the radial direction of said specimentable.
 6. The apparatus of claim 1 or 2, further comprising an auxiliaryjig interposed between said surface plate and said specimen table, forfixing them to each other by vacuum suction.
 7. The apparatus of claim 1or 2, wherein said specimen table is made of the same material as thatfor said specimen.
 8. The apparatus of claim 1 or 2, wherein saidspecimen table is made of an isotropic material.
 9. The apparatus ofclaim 8, wherein said specimen table is made of glass.
 10. The apparatusof claim 9, wherein said specimen table is made of synthetic quartzglass.
 11. The apparatus of claim 8 wherein said specimen table is madeof ceramics.
 12. The apparatus of claim 1 or 2, wherein a shielding casesurrounding said specimen table and said linear gauge is mounted on saidvibration isolation table.
 13. A method for measuring the thickness of aspecimen by use of a linear gauge provided with a surface plate and ameasuring element, said method comprising the steps of: (a) bringingdown said measuring element of said linear gauge from above into contactwith a centrally-disposed circular protrusion of a specimen tablemounted on said surface plate to measure the position of said measuringelement as a first position, said centrally-disposed circular protrusionhaving a diameter sufficiently smaller than said specimen; (b) mountingsaid specimen on said centrally-disposed circular protrusion andbringing down said measuring element of said linear gauge from aboveinto contact with said specimen to measure the position of saidmeasuring element as a second position; and (c) calculating thethickness of said specimen from the first and second positions.
 14. Themethod of claim 13, wherein: said step (a) includes a step ofcalculating a first distortion caused by said contact of said measuringelement with said centrally-disposed circular protrusion of saidspecimen table, based on the pressure between said measuring element andsaid centrally-disposed circular protrusion of said specimen table andthe properties of material for said specimen table and said measuringelement; said step (b) includes a step of calculating a seconddistortion caused by said contact of said measuring element with saidspecimen, based on the pressure between said measuring element and saidspecimen and the properties of material for said specimen and saidmeasuring element; and said step (c) includes a step of correcting themeasured thickness based on the difference between said first and seconddistortions.
 15. The method of claim 13, wherein said specimen table ismade of the same material as that of said specimen.